Closure mechanism of the A1 and A2 modes in jet screech

Abstract

This paper explores the screech closure mechanism for different axisymmetric modes in shock-containing jets. While many of the discontinuities in tonal frequency exhibited by screeching jets can be associated with a change in the azimuthal mode, there has to date been no satisfactory explanation for the existence of multiple axisymmetric modes at different frequencies. This paper provides just such an explanation. As shown in previous works, specific wavenumbers arise from the interaction of waves in the flow with the shocks. This provides new paths for driving upstream-travelling waves that can potentially close the resonance loop. Predictions using locally parallel and spatially periodic linear stability analyses and the wavenumber spectrum of the shock-cell structure suggest that the A1 mode resonance is closed by a wave generated when the Kelvin–Helmholtz mode interacts with the leading wavenumber of the shock-cell structure. The A2 mode is closed by a wave that arises owing to the interaction between the Kelvin–Helmholtz wave and a secondary wavenumber peak, which arises from the spatial variation of the shock-cell wavelength. The predictions are shown to closely match experimental data, and possible justifications for the dominance of each mode are provided based on the growth rates of the absolute instability.

A unifying theory of jet screech

“…In this paper, we demonstrate the generality of the result of Nogueira et al. (2022 a ), showing that it not only provides an explanation for staging of the modes in axisymmetric jet screech, but in fact accounts for all modal staging behaviour in screeching jets. Instead of an argument based on linear stability theory, here we provide evidence based on analysis of experimental data.…”

“…From Nogueira et al. (2022 a ), a full consideration of the shock-cell structure is required to predict staging behaviour, and a spectral representation is an effective means to achieve this. In figure 3, time-averaged visualizations of the gradient from both datasets are presented, along with the absolute value of their accompanying streamwise Fourier transforms ().…”

“…A reconciliation of the two equations and an explanation for mode staging behaviour in the context of Tam & Tanna (1982) was provided in the work of Nogueira et al (2022a); in this work the A1-A2 staging was correctly predicted without the inclusion of any empiricism. At the core of this prediction was a consideration of the axial variation of the shock-cell structure, which in the spectral domain manifests as a series of suboptimal peaks k s 2:n in addition to the fundamental k s 1 .…”

“…In the original formulation, the wavenumbers in the series are restricted to those arising from the solution of the vortex-sheet dispersion relation at zero frequency, whereas in the present application they are just an empirical representation of the mean shock structure in the spectral domain; all wavenumbers are permitted. Critically, Nogueira et al (2022a) demonstrated that the A1 mode of jet screech was associated with the KH wavepacket interacting with the fundamental peak, while the A2 mode was associated with an interaction with the first suboptimal. Both a local linear stability framework using experimental data and a consideration of absolute instability via the spatially periodic linear stability analysis framework produced robust predictions across the A1-A2 range of jet screech on this basis.…”

“…Critically, Nogueira et al. (2022 a ) demonstrated that the A1 mode of jet screech was associated with the KH wavepacket interacting with the fundamental peak, while the A2 mode was associated with an interaction with the first suboptimal. Both a local linear stability framework using experimental data and a consideration of absolute instability via the spatially periodic linear stability analysis framework produced robust predictions across the A1–A2 range of jet screech on this basis.…”